Abstract

The use of the asymptotic treatment for the wedge diffraction problem established long ago by
Pauli [Phys. Rev.
54, 924 (1938)]
is here revisited and proposed in the character of a powerful computational tool for accurately retrieving the total electromagnetic field even in the near zone. After proving its factorial divergent character, the Pauli series is summed through the Weniger transformation, a nonlinear resummation scheme particularly efficient in the case of factorial divergence. Numerical results are carried out to show the accuracy and effectiveness of the proposed approach.

It should be noted that in the original paper, Pauli used the opposite convention; i. e., the temporal factor had the form exp(+iωt). For this reason, the subsequent formulas are the complex conjugate of those written in .

F. Gori, "Diffraction from a half-plane. A new derivation of the Sommerfeld solution," Opt. Commun. 48, 67-70 (1983).
[CrossRef]

We use, as far as possible, a notation similar to the original one adopted in .

If, on the contrary, the illumination produces no geometrical shadow, to obtain a regular representation also at the second reflection, it is sufficient to change φ into φ−2πn in all the following equations.

When z is a real negative, the integral in Eq. must be intended in the Cauchy principal value sense. This is related to the fact that the line arg z=π represents a branch cut for the exponential integral function .

Q. J. Mech. Appl. Math.

Other

It should be noted that in the original paper, Pauli used the opposite convention; i. e., the temporal factor had the form exp(+iωt). For this reason, the subsequent formulas are the complex conjugate of those written in .

When z is a real negative, the integral in Eq. must be intended in the Cauchy principal value sense. This is related to the fact that the line arg z=π represents a branch cut for the exponential integral function .

We use, as far as possible, a notation similar to the original one adopted in .

If, on the contrary, the illumination produces no geometrical shadow, to obtain a regular representation also at the second reflection, it is sufficient to change φ into φ−2πn in all the following equations.

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